Question: Complete the square to solve for $x$. $x^{2}-2x-3 = 0$
Begin by moving the constant term to the right side of the equation. $x^2 - 2x = 3$ We complete the square by taking half of the coefficient of our $x$ term, squaring it, and adding it to both sides of the equation. Since the coefficient of our $x$ term is $-2$ , half of it would be $-1$ , and squaring it gives us ${1}$ $x^2 - 2x { + 1} = 3 { + 1}$ We can now rewrite the left side of the equation as a squared term. $( x - 1 )^2 = 4$ Take the square root of both sides. $x - 1 = \pm2$ Isolate $x$ to find the solution(s). $x = 1\pm2$ So the solutions are: $x = 3 \text{ or } x = -1$ We already found the completed square: $( x - 1 )^2 = 4$